To increase assay throughput and allow more efficient use of DNA samples, simultaneous amplification of many target nucleic acids in a sample of interest can be carried out by combining many specific primer pairs with a sample of interest and then subjecting the sample to polymerase chain reaction (PCR) conditions in a process known in the art as multiplex PCR. However, when multiple specific primer pairs are added to the same PCR reaction, non-target amplification products may be generated, with the risk of generating such products increasing with increasing numbers of specific primer pairs employed. These non-target “amplicons” significantly limit the utility of the amplification product for further analysis and/or assays. Even with careful attention paid to the design of the primers, multiplex PCR is typically limited to 10-20 specific primer pairs in a single multiplex reaction before amplification yield is compromised by the accumulation of non-target amplicons (see, e.g., Syvanen, A C., Toward genome-wide SNP genotyping. Nature Genetics (2005) 37 Suppl: p. S5-10; and Broude, N. E., et al., Multiplex allele-specific target amplification based on PCR suppression. PNAS (2001) 98(1): p. 206-11). As such, there is a continued need for improved methods to reduce the impact of non-target amplicon generation in multiplex PCR.